This is a continuation of last year's work on the mechanisms of movement of the motor protein kinesin on a microtubule (a periodic biopolymer made of identical monomer subunits). A single kinesin molecule when attached to a microscopic plastic bead can move itself and carry the bead with it unidirectionally on a microtubule by catalyzing the hydrolysis of ATP. The movement can be carried out by both one-headed and two-headed kinesin molecules. In the two-headed case, the simplest mechanism for movement is the so-called "hand-over-hand" model, in which the two heads alternate between attached and detached states in an ordered sequence (like the walking motion of a human being). Exactly how a one-headed kinesin moves the bead is not clear. Our research in this year was centered on this question. Our research has yielded two findings. First, using the theory of "cross-bridge" formalism for muscle contraction, we have found that the movement of a bead on a microtubule powered by a single one-headed kinesin is equivalent to the movement of a Brownian particle in a fluctuating periodic potential field. Therefore, the first step in understanding the mechanism of kinesin movement is to solve the Brownian motion problem. The movement of a Brownian particle in a fluctuating periodic potential field has been solved before for the case that the potential within each period is asymmetric. For biological motors, the potential is symmetric. No studies of this kind on symmetric potentials have been reported up to now. We are the first to solve this problem. We have found that, in order for a Brownian particle to execute a biased movement in a fluctuating periodic symmetric potential, the following two conditions have to be satisfied. First, the potential must fluctuate among three or more translationally-shifted "potential states". Second, the fluctuation process must be done in such a way that a net cycling around the states exists. Using the model we developed, we found that a single one-headed kinesin indeed can move a bead on a microtubule if the kinesin can attached to the microtubule in two distinct conformations with different tilting angles relative to the axis of the microtubule. We also have developed a formalism for calculating the movement velocity of the particle at long time when the kinetic parameters of the fluctuation process are given. The formalism should be useful in studying in vitro motility measurements in which the bead is powered by one-headed kinesin molecules.